Distributacalcul (version 0.4.0)

Logarithmic: Logarithmic Distribution

Description

Logarithmic distribution with probability parameter \(\gamma\).

Usage

dLogarithmic(x, prob)
pLogarithmic(q, prob, lower.tail = TRUE)
expValLogarithmic(prob)
varLogarithmic(prob)
VatRLogarithmic(kap, prob)
mgfLogarithmic(t, prob)
pgfLogarithmic(t, prob)

Value

Function :

• dLogarithmic gives the probability density function (PDF).

• pLogarithmic gives the cumulative density function (CDF).

• expValLogarithmic gives the expected value.

• varLogarithmic gives the variance.

• VatRLogarithmic gives the Value-at-Risk.

• mgfLogarithmic gives the moment generating function (MGF).

• pgfLogarithmic gives the probability generating function (MGF).

Invalid parameter values will return an error detailing which parameter is problematic.

Arguments

x, q

vector of quantiles.

prob

probability parameter \(\gamma\).

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

kap

probability.

t

t.

Details

The Logarithmic distribution with probability parameter \(\gamma\) has probability mass function : $$Pr(X = k) = \frac{-\gamma^{k}}{\ln(1 - \gamma)k}$$, for \(k = 0, 1, 2, \dots\), and \(\gamma \in (0, 1)\)].

Examples

dLogarithmic(x = 3, prob = 0.2)

pLogarithmic(q = 3, prob = 0.2)

expValLogarithmic(prob = 0.50)

varLogarithmic(prob = 0.50)

VatRLogarithmic(kap = 0.99, prob = 0.2)

mgfLogarithmic(t = .2, prob = 0.50)

pgfLogarithmic(t = .2, prob = 0.50)